Such header plates are used in particular in radiators which are employed for the cooling of supercharging air in motor vehicles, in which the supercharging air, which flows in the header and in the tubes, is at a high pressure and at a temperature which may exceed 100.degree. C. This gives rise to mechanical and thermal stresses in the header plate which, especially when the latter is made of aluminium alloy, can give rise to the formation of cracks along the generatrix of the curved region, the latter having already undergone fatigue during the bending operation in which it was initially formed.